Effects of strain rate on mode II interlaminar fracture toughness in carbon-fibre/epoxy laminated composites

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Effects of strain rate on mode II interlaminar fracture toughness in carbon-fibre/epoxy laminated composites

T. Kusaka, Y. Yamauchi, T. Kurokawa

To cite this version:

T. Kusaka, Y. Yamauchi, T. Kurokawa. Effects of strain rate on mode II interlaminar fracture

toughness in carbon-fibre/epoxy laminated composites. Journal de Physique IV Proceedings, EDP

Sciences, 1994, 04 (C8), pp.C8-671-C8-676. �10.1051/jp4:19948102�. �jpa-00253343�

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JOURNAL DE PHYSIQUE IV

Colloque C8, supplkment au Journal de Physique 1.1, Volume 4, septembre 1994

Effects of strain rate on mode I1 interlaminar fracture toughness in carbon-fibrelepoxy laminated composites

T. Kusaka, Y. Yamauchi* and T. Kurokawam*

Hyogo Prefectural Institute of Industrial Research, 3-1-12 Yukihira-cho, Suma-ku Kobe 654, Japan

*

Dept. of Precision Engineering, Osaka University, 2-1 Yamadaoka Suita 565, Japan

**

Dept. of Aeronautical Engineering, Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto 606-01, Japan

RQsumB: La relation entre la vitesse de deformation et la resistance F la rupture interlaminaire en Mode II d'un composite lamink CF/epoxy a BtB examine par des experiences en flexion d'un composite prQdelamin6 & son extremitk en mode dynamique (dynamic ENF test) utilisant l'essai SHPB. Les ondes incidentes de forme exponentielle ont Cvitk le problitme de vibrations parasites en flexion. L'analyse dynamique par les BlCments finis confirme que la formule estimee peut Btre utilisee pour la r'esistance F la rupture Mode 11, aussi bien en dynamique qu'en statique. Les rCsultats experimentaux montrent que la. rksistance F la rupture en Mode II a tendance B diminuer avec l'accroissement de la vitesse de deformation en cisaillement. Ceci serait dB aux diffkrences entre ruptures dynamique et statique.

Abstract: The strain rate dependence of Mode II interlaminar fracture toughness in unidirectional CF/epoxy composite laminates was studied by the dynamic End Notched Flexure (ENF) test using a Split Hopkinson Pressure Bar (SHPB) system. The experimental technique using a ramped incident wave was adopted to suppress the influence of the flexural vibration of the specimen. Finite element analysis confirmed that the estimating formula for static Mode II fracture toughness can be applied to dynamic Mode II fracture toughness as well. The experimental results indicated that the Mode II fracture toughness tends to decrease with increasing shear strain rate. This tendency is thought to be due to the fractographic differences between static and dynamic fractures.

1. INTRODUCTION

In composite structures, the small delamination cra.cks introduced during manufacturing or work- ing processes can cause catastrophic failure. Recently, many studies applying linear fracture mechan- ics to this kind of problem have been conducted, and the DCB (Double Cantilever Beam) test for the opening mode (Mode I), the ENF (End Notched Flexure) test[l,2] for the shearing mode (Mode

II)

and t h e CLS (Cracked Lap Shear) test for the mixture of Modes I and

II

have been performed as standard experimental methods. Applying these, the interlaminar fracture toughness and the crack propagation behaviour under static loading have been studied in various kinds of composite laminate.

But relatively few experimental results under dynamic or impact loading have been reported[3,4]. In the present study, the SHPB (Split Hopkinson Pressure Bar) technique was employed t o carry out dynamic ENF tests, and the strain rate dependence of Mode

II

interlaminar fracture toughness in two typical unidirectional CF/epoxy composites was investigated.

2. EXPERIMENTAL PROCEDURE 2.1 Static ENF Test

Static ENF tests were carried out a t shear strain rates ranging from to lo-' sec-I using universal testing instruments. The ENF test is one of the most general methods for measuring Mode

II

interlaminar fracture toughness in composite laminates. As shown in Figure 1, it is essentially Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:19948102

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JOURNAL DE PHYSIQUE IV

Fibre orientation 9 /

Figure 1: End notched flexure specimen.

Figure 2: Dynamic ENF test apparatus.

a three-point flexure test using a. coupon specimen with an embedded through-width delamination placed at the 1a.minate midsurface where the interlaminar shear stress is greatest; Gillespie et al.[l]

have proved by FEM analysis that the ENF test is a pure Mode I[ fracture test within the limits of small deformation.

2.2 Dynamic ENF Test

Dynamic ENF tests were carried out at shear strain rates ranging from 10' to l o 2 sec-' using the SHPB system as shown in Figure 2. The experimental technique placing a soft metal buffer on the collision face between the striker bar and the input bar was used. This was effective to generate a ramped incident wave and to suppress the high frequency vibration of the specimen at the early stage of loading. A few examples of histories of ramped incident waves are shown later in Figure 6 ( 4 .

2.3 Specimen Preparation

Two typical CF/epoxy composite materials were examined in the present study. One is T300/2500 (Toray), which has a standard epoxy matrix of 100 MPa in strength. The other is Q-C133 (Toho rayon), which has a toughened epoxy matrix of 140 MPa in strength by containing a thermoplastic resin. The T300/2500 panels were processed in a heat press and the Q-C133 panels were processed in a.n autoclave according to the manufacturers' recommended cure cycles (Q-C133: at 180 O C ,

T300/2500: a t 120 "C). Both were machined to specimens with a diamond saw with the geometries shown in Table 1. The initial cracks were introduced by inserting a 25 pm thick Teflon film in the lay-up process and precracked with a. cutter blade to avoid the influence of the resin-rich region at the film's tip.

3. DATA REDUCTION

Table 1: Mechanical properties and geometries of the ENF specimen.

3.1 Load

The applied load history at the centre of the specimen, PCni(t), and the reaction force history a t the two supporting points of the specimen, P,,,(t), are given by,

Q-C133 T300/2500

where u ~ ( t ) and u ~ ( t ) are the histories of the incident and reflected stress waves in the input bar, and u ~ ( t ) is the sum of the transmitted stress waves in the two output bars (compressive stress and load are defined to be positive in this paper), and A;,, and A,,, are the cross sectional area of the

olume frac.

Vf (%) 54 56 Youn 's mod.

E, f ~ F ' a ) 140 120

Shear mod.

G,, (GPa) 4.0 3.2

Stacking

sequence [ o f ] [ozol

Dimensions (mm) 2.

60 30

2h 2.6 5.1

w 5 5

a 15 7.5

Lo 70 40

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input and output bars. Typical histories of P,,t(t) and P,,,(t) are shown in Figure 3. Generally the

equilibrium of these forces does not hold good in 300-

----

dynamic tests, unlike static tests, because of inertia

-

forces. However, utilizing a ramped incident wave, the influence of the inertia force becomes small and

2

the difference between Pcnt(t) and P,,,(t) can be supposed to be negligible near the time of 'fracture

initiation. Thus the load applied to the specimen, 100 200 300 400 P ( t ) , can be approximated by,

Time t , psec

P ( t )

-

^Pcnt(t)

-

^Psw(t)

t2)

^Figure^3:Histories of the applied load, Pent, and 3.2 Displacement the reaction force, PSup, in a dynamic ENF test.

In accordance with one-dimensional elastic wave theory, the particle velocities at the right end of the input bar, vi,,(t), and at the left end of the output bars, vout(t), are given by,

where p,,,~,,, and poutcout are the acoustic impedances of the input and output bars. Except at the early stage of loading, the specimen can be considered to keep contact with the input bar and the output bars because the values of

P,,,(t)

and P,,,(t) are not zero. Thus the total deflection of the specimen, S(t), is,

a(t) =

J

^(utnp(t)^-^vout(t))^dt ⁽⁴⁾

3.3 M o d e

II

S t a t i c F r a c t u r e Toughness

Using the compliance technique based on Griffith's fracture criteria, the static energy release rate, G, is given by[5],

where C is the compliance of the specimen and A is the area of the crack. Calculating the value of C theoretically, the Mode II critical energy release rate, Grrc, is reduced to,

where w, h, a, E, and Gx, are the width, the half of thickness, the initial crack length, the Young's modulus and the shear modulus of the specimen, respectively. PC is the load at fracture initiation;

here, PC was considered as the maximum value of applied load because the matrixes of the present ma.terials were relatively brittle and fracture grows unstably[2]. The constant, a , can be determined by FEM analysis. Equation (6) is based on beam theory with shear deformation included[2] and applied to the specimens of Q-(2133, and Equation (7) is based on plate theory[5] and applied to the specimens of T300/2500, whose values of h / a were comparatively large.

3.4 M o d e

II

D y n a m i c F r a c t u r e Toughness

In dynamic ENF tests, the following two points must be taken into account when estimating the value of GIIc by the compliance technique; firstly the dynamic deformation mode of the specimen is generally different from the static mode; secondly the kinetic energy of the specimen may affect

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the estimation of the dynamic fracture toughness. With respect to the first problem, the dynamic deformation mode was the same as the static mode within the present experimental conditions, as is discussed in the next section. With respect to the second problem, Smiley et a1.[3] have estimated the kinetic energy contribution from,

= G$$

+

0 . 0 7 8 ~ h 8 ~ ( 8 )

where G$'F is a, true dynamic fracture toughness and G ; g is the apparent fracture toughness evalua.ted by Equation (6) or (7) derived by the compliance technique. The second term of the right-hand side ranged from 0.2 to 3

5%

in the present specimens, so its influence was neglected and the equation estimating G$$ was applied to estimate the value of ~ $ 2 " as well. The validity of this approximation will be confirmed in the next section by means of FEM analysis.

3.5 Shear Strain Rate

To discuss the dynamic properties of materials, a parameter indicating the rate of deformation should be defined. Here, the shear strain rate at the midsurface of the specimen, +(t), was used and estimated by,

for some oscillation. Therefore the dynamic defor- Displacement 6 , mm

mation mode can be considered to be the same as ~i~~~~ 4: ~ ~ ~ d - dresponse i ~in ~a dy. l ~ ~ ~ ~ ~ ~ t the static mode. It is valid, therefore, to calculate ENF test.

the compliance of the specimen by static beam or plate theory.

4. RESULTS AND DISCUSSION 400 ^I ^I

/

I /

-

Experimental ^,I 4.1 Load-Displacement Response

300-

----

Theoretical ^,^/ ^/

-

A typical load-displacement curve reduced by 2

-

4.2 Computational Approach I

From Irwin's theory of fracture[7], the energy

absorbed in the process of cra.ck growth is equal to

o L - ~

A

the amount of work required to close the crack to

its original length. This theory is very convenient Figure 5: Finite element model at the crack tip.

to FEM analysis and used as virtual crack closure technique[8]. When the crack is modeled in two-dimensional elements as shown in Figure 5, the Mode

II

energy release rate, GgC, is given by, the above procedures in a dynamic ENF test is _{4 200}_a

-

shown in Figure 4. The solid line shows an ex-

perimental load-displacement curve and the dotted 4 100

-

line shows the theoretical curve evalua.ted by static

C C - 1

G~~ -

2wna

^TE(UC^-^{U D )} ⁽¹⁰⁾

where TE is the x-component of the nodal force at the node E, and u c and U D are the x-components of the displacement of the nodes C and D. This formula can evaluate Mode I1 energy release rate directly without the need to consider the dynamic deformation mode of the specimen. In the present study, the dynamic ENF test was simulated by this method. Sorne examples of calculated results for reciprocal GgT histories nondimensionalized by GgC are shown in Figure 6 (b), where GgT is the apparent energy release rate evaluated by Equation (7) and the incident waves were assumed to have the ramped velocity form shown by the thick solid lines in Figure 6 (a) and given by,

-

~ ( t ) = VO {I - exp

(- $1 }

beam theory. The experimental curve shows overall ^I

agreement with the static theoretical curve except ^0.5 ^1.0 ^1.5 ^2.0

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where T is a rise-time parameter. In Figure 6 (a), the thin solid and dotted lines show the experimental incident waves with and without a soft metal buffer, respectively. Figure 6 (b) shows that the value of GgT converges into the value of Ggc for T

>

^{30 after}t ⁼100 psec. Hence the static formula derived from the compliance technique can also be applied to estimate the dynamic fracture toughness if a ramped incident wave is applied.

Experiment (with buffer) Experiment (without buffer s"

--. -

Input data for FEM b (T = 5,15,30,50,70 jisec)

., 0 ::

2.0 ^I

--.

^---^T⁴⁵^psec ^I

50 100 150 200

Time t , psec Time t

,

psec

(a) Incident waves (b) Energy release rate

Figure 6: Incident wave histories with various rise-times and histories of the dynamic energy release rate,

G S ~ ,

^{by FEM.}

4.3 Effects of Strain Rate

The relationship between the fracture toughness, Grrc, and the shear strain rate at crack initiation, j c , is shown in Figure 7, where 0, and 0 are the data in Q-C133, T300/2500 and AS4/2220- 3[4], respectively. Figure 7 indicates that the Mode I[ fracture toughness tends to decrease with increasing shear strain rate and that the value of GrIc a t j.C = lo2 sec-l is approximately 20 % lower than the value at jc = lo-' sec-' in each material equally.

Shear strain rate j , l/sec

Figure 7: Strain rate effects on Mode ^I[fracture toughness.

4.4 Fractography

Figure 8 shows delamination surfa.ces in the ENF specimens at a distance of 1 mm from the initial crack tip observed with a SEM; (a) is a static fracture surface ( j c = 9.2 x sec-') and (b) is a dynamic fracture surface (-jc = 3.8 x 10' sec-l), and the crack propagated from the top to the bottom. The hackle-looking fracture surfaces due to ductile fracture in the matrix resin are observed at low strain rates. The smooth fracture surfaces due to debonding at the interface between reinforcing fibres and matrix resin are mainly observed, and the matrix resin is only deformed a little,

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PHYSIQUE IV

at high strain rates. These fractographic differences are supposed to have much to do with the above tendency, that is, the dynamic strength of bonding between reinforcing fibres and matrix resin may be lower than the sta.tic strength. The fibre surfaces of both materials were treated in standard processes, but the influence of the surface treatment on the dynamic strength has not been clear yet.

(a) Static (b) Dynamic

Figure 8: Typical fracture surfaces in Q-C133.

5. SUMMARY AND CONCLUSIONS

Dynamic ENF tests were performed in unidirectional CF/epoxy composite laminates using the SHPB system in order to estimate the Mode

II

interlaminar fracture toughness a t high strain rates.

It has been shown that the Mode

II

dynamic interlaminar fracture toughness can b e estimated by means of the compliance technique based on beam or plate theory as in the case of static ENF tests if a ramped incident wave with an appropriate rise-time is applied, thereby suppressing the high frequency flexural vibration of the specimen. This was confirmed by the FEM analysis using the virtual crack closure technique.

Using t h e above procedures, the strain rate dependence of Mode

II

interlaminar fracture toughness in two typical CF/epoxy composites was investigated. The results indicated that the Mode II interlaminar fracture toughness tends to decrease with increasing strain rate; the fracture toughness, Grrc, a t t h e shear strain rate

i.c

= to2 sec-' was approximately 20 % lower than the value a t jc = lo-' sec-' in each material.

The SEM observations indicated that the above tendency is caused by the fractographic differences; the hackle-looking fracture surfaces due to ductile fracture in the matrix resin are observed a.t low strain rates, but the smooth fracture surfaces due to debonding a t the interface between reiforcing fibres and t h e matrix resin are mainly observed a t high strain rates.

REFERENCES

[I] Gillespie J. W. Jr., Carlsson L. A. and Pipes R. B., Comp. Sci. B Tech. 26 (1986) 177-197.

[2] Carlsson L. A., Gillespie J. W. Jr. and Pipes R. B., J. Comp. Mat. 20 (1986) 594-605.

[3] Srniley A. J. and Pipes R. B., Comp. Sci. B Tech. 29 (1987) 1-15.

[4] Maikuma H., Gillespie J. W. Jr. and Wilkins D. J., J. Comp. Mat. 24 (1990) 124-149.

[5] Carlsson L. A. and Pipes R. B., Experimental Characterization of Advanced Composite Materials (Prentice-Hall, New York, 1987) Chap. 2.

[6] Carlsson L. A., Gillespie J. W. Jr. and Whitney J. M., Proc. 1st Conf. on Comp. Mat., (Technomic Publishing, 1986) pp.421.

[7] Irwin G. R., Handbuch der Physik (Fliigge Edition, Berlin, 1958) pp.551.

[8] Rybicki E. F. and Kanninen M. F., Eng. Fracture Mech. 9 (1977) 931.